Electric simulators of arbitrary functions



July 14,A 1959 J. E. MARTIN 2,895,045

ELECTRIC smULAToRs QF ARBITRARY FUNCTIONS Filed Fepgls, 1954 United States Patent iiice '2,895,046 Patented July 14, 1959 ELECTRIC SIMULATORS `F ARBITRARY FUNCTIONS y Jacques Edouard Martin, Paris, France, assignor to S0- tlrriete dElectronique et dAutomatisme, Courbevoie,

rance iApplication February 15, 1954, Serial No. 410,119

Claims priority, application France March 19, 1953 2 Claims. (Cl. Z50-27) The present invention relates to electric simulators of arbitrary functions, i.e. electric devices which may be given any desired transfer characteristic corresponding to an arbitrary though adjustable law of variation of a geometrical curve which has been previously reduced, by graphical analysis, to a combination of elementary functions each of which represents a portion of a straight line having a predetermined slope. By transfer characteristic is meant the curve obtained by plotting the values of an output voltage as ordinates, against the values of at least one input voltage, as abscissa.

Copending application Serial Number 290,588, now Patent No. 2,831,107, filed May 22, 1952, led by Franois Henri Raymond, Pierre Louis Chapouille and Jacques Edouard Martin and assigned to the same assignee as 'the present application, provided an electric simulator of an arbitrary function of at least one variable, composed of elementary functions each of which represents a portion of a straight line of determined slope. In this simulator at least one variable representative Voltage is supplied to at least an array of transfer stages having input means connected to lsuch voltage supply and each including means for adjusting the attenuation of such voltage to apredetermined ratio depending upon coefficients of the elementary functions. Atleast some of these transferk networks includerneans for limiting their output voltages to a predetermined value depending upon coeicients of the elementary functions, such transfer stages having outputs connected to the input of at least one summation amplifier.

Such an arrangement apparently requires one separate transfer network for the electric representation of each portion of a straight line ofdetermined slope. Each transfer network includes a calibrated series resistor connected to a further calibrated series resistor forming-part of an input coltage mixer for aV summation amplifier. Further, each transfernetworkin addition to being provided with means for limiting its output voltage Ito a predetermined value, has a shunt branch; including at least one unidirectionally conducting element, preferably a vacuum diode tube one electrode of which is connected to the end of the first of these series 'resistors and the other is connected to a predetermined voltage supply.

The present invention, which constitutes a continuation in part of the above mentioned copending application, has for its object to provide a more simple and economical arrang'ementforV an electric simulator of an arbitrary function of the kind specified above.

Another object ofthe invention is to provide an improved arrangement of transfer networks for an electric simulator of an arbitrary function of the kind specified whereby a substantial reduction in the number of transfer networks is achieved while a determined overall efficiency and simulator accuracy are maintained. Alternatively, in accordance with the invention a greater efficiency a greater accuracy are achieved with a determined nurnber-of component transfer networks. Y v

A further object of the invention is to provide an improved transfer network for an electric simulator of an arbitrary function of the kind specified, the Itransfer characteristic of which represents at least Itwo and possibly more than two portions of straight lines of different predetermined slopes, each portion of a straight line abutting the neX preceding one in the elementary transfer characteristic of this transfer network.

According to the invention, in an electric simulator of an arbitrary function of the kind specified, at least some of the component transfer networks include each a series resistor in its limiting shunt branch, between the connection point of that shunt branch and the corresponding electrode of its unidirectionally conducting element. In this way, the transfer characteristic of this network is made to consist of a rst portion of a straight line starting from the origin with a first predetermined slope, and a following portion of a straight line starting from the end point of the first slope and having a second predetermined slope; the end point corresponds to the voltage value for which the unidirectionally conducting element is activated.

According to another object of the invention, further, the series resistor is tapped at'intermediary points and each tap is connected over a separate unidirectionally conducting element to a separate voltage supply. In this Way the transfer characteristic of the transfer network is made to consist of as many portions of straight lines of different predetermined slopes as there are provided unidirectionally conducting elements, and of an additional portion of a straight line having a predetermined different slope defined by the value of the portion of the resistor inserted between the connection point and the first tap ofthe series resistor.

These and other objects of the invention will now be described more fully and by way of examples with reference to the accompanying drawings, wherein:

Fig. 1 shows a relatively simple arrangement of a transfer network for an electric simulator of an arbitrary function of the kind specified, according to the present invention;

Fig. 2, shows the transfer characteristic of the network of Fig. 1; f

Fig. 3 represents a combination of transfer networks having the same transfer characteristic in an electric simulator such as disclosed in the above mentioned copending application;

Fig. 4 shows an extension of the embodiment of Fig. 1, according to the invention;

*Fig 5 vshows the transfer characteristic of the network of Fig; 4;

"Fig 6 shows another extension of the embodimentof Fig. 1 according to the invention; and,

Fig. 7 shows the transfer characteristic of the embodiment of Fig. 6.

From these illustrations of the invention many other lay-outs of transfer networks for an electric simulator of an arbitrary function of the kind specified and such as disclosed in the above mentioned copending application can be developed without departing from the scope of the invention.

In Fig. 1, a transfer network is shown to consist of' series resistor 17 connected at point 19 toa Ifurther series resistor 18 forming part of the input voltage mixer of a summation amplifier. Such summation amplier is illustrated by vamplier 22 and feedback resistor 2.3. The

values of the three resistors 17, 18 and 23, may be conresistor 17. If x denotes the variable voltage atpint 7 and al the predetermined slope which would be the slope of the transfer characteristic of the network if it would only contain the above elements, the slider 14 is so adjusted that the voltage applied to resistor 17 is x.tan al. This slope al is` that of the line OB in Fig. 2.

A calibrated reference voltage is applied to terminal 5 and fed through an adjustment potentiometer 9 for instance, over slider 13 to the cathode of a vacuum tube diode 15. The anode of tube 15 is connected to point 19 through a series resistor 100. The voltage value on slider 13 is adjusted to be proportional to yl=x1.tan al, viz. the ordinate value limiting, as shown in Fig. 2, the portion of a straight line starting from origin O and ending at point A for an abscissa value x1.

If resistor 100 were omitted, as for example in transfer networks such as disclosed in the above mentioned copending application, for any value of x greater than x1, the output voltage would be on the portion of a straight line AC which is parallel to the abscissa axis of the characteristic. Diode 15 would then be conducting and, at 19, the voltage value x1.tan al, substituted for the voltage value x.tan a1. If however, as in the present case, the resistor 100 is provided the characteristic does not present a zero slope in that part of the plane. Once diode 15 becomes conducting, the transfer characteristic presents a slope a2, namely, a straight line portion AD in Fig. 2.

If R100 denotes the value of resistor 100 and R17 the value of resistor 17, which is also the value of the resistor 18, and if K denotes the value of the ratio between the slopes after and before diode 15 is activated, viz.

the following relation exists between R100 and R17- (ii) l The significance of Relation ii is apparent: For any definite value of resistor 100 there is obtained a definite slope a2 ofthe portion of a straight line AD. Conversely, to adjust the slope of AD to a predetermined value, it will be suicient to provide a value R100 for resistor 100 derived from Relation for a ratio k such as derived from Relation i.

`In order to visualize the simplification in structure of an electric simulator of the kind specified and brought about by putting the present invention into practice, Fig. 3 shows the lay-out of part of such a simulator which is required to obtain the same characteristic as that illustrated in Fig. 2 without realising the invention. It is apparent that three transfer networks are required in such a case.

A rst network I is of the same structure as that disclosed in Fig. 1 except that resistor 100 is omitted. This network has the transfer characteristic OAC of Fig. 2. A second network II mainly comprises resistors 70 and 71; resistor 71 forms part of the input mixer of the summation amplier. The variable voltage is applied to this second network from slider 90 of potentiometer 94 fed from the same terminal 7 as the first network. Slider 90 is so adjusted as to impart to the variable voltage an attenuation proportional to tan a2. 'I'he third network III is of a structure similar to that of Fig. 1 but the direction of conductibility of its own diode tube 95 is reversed; the cathode is connected to point 99 of interconnection between resistors 97 and 98 (the latter forming part of the input mixer of the summation amplier). Resistor 97 receives its supply voltage from slider 89 of a potentiometer 93 which receives at terminal 8 the variable voltage with a polarity opposite to that of the variable voltage applied at 7. The anode of diode 95 is connected to slider 113 of a potentiometer 109 which receives the reference voltage at terminal 6 with a polarity opposite to that of the reference Voltage at 5. Sliders 90 and 113 are adjusted to positions corresponding to those of sliders 14 and 13 in network I.

k=tan 112/ tan a1 The transfer characteristic of the network II is developed as a portion of a straight line OE, Fig. 2, and the transfer characteristic of network III is represented by OPG, Fig. 2. The overall characteristic of the arrangement of Fig. 3 is that resulting from the addition of the three characteristics OB, OE and OFG, viz. OAD. Such a characteristic OAD is derived from a single network if this network is designed in accordance with the present invention.

If now, Fig. 4, a second diode 115 is connected to point 19, and the cathode of diode 115 receives from slider 123 of a further potentiometer 119 `fed by reference voltage at 5, a voltage of a value y2 higher than y1, the transfer characteristic will be as shown in Fig. 5. As soon as the variable voltage at 7 becomes greater than y2, the point of line AD `for which y=y2, the output voltage of the transfer network is limited to this value y2. The overall characteristic of the network contains the portions OA and AH and HJ parallel to the abscissa axis.

If for illustration sake, resistor is replaced by or formed of three series resistors 101, 102 and 103, Fig. 6, two further diodes 215 and 315 may be connected to the connection points between these resistors, in addition to diode tubes 15 and 115. The cathodes of diodes 215 and 315 receive reference voltages of values y3 and yg intermediate between the values y1 and y2, through potentiorneters 219 and 319 receiving the reference voltage at 5. The overall or resulting transfer characteristic therefore will be as shown in Fig. 7, containing the portions of straight lines OA, of slope tan a1, AK, of slope tan a4, KL, of slope tan a3, LH, of slope tan a2, and HI, of zero slope.

Any other subdivision of `resistor 100 can be provided to obtain a transfer characteristic of any other number of portions of straight lines. The sole restriction lies in the condition that the value of any of the resistors such as 101, 102, must not be of the same order as the internal resistance of the diodes. This condition may also be stated as follows: 'Ihe ratios between consecutive slopes of the transfer characteristic must not be too high.

Considering for instance the circuit of Fig. 6 and the characteristic of Fig. 7, the following relations may be established between the slopes of straight line portions OA, AK, KL and LH:

tlIl [l2: a1 tan a3: (1/2 .tan a1 tan a4: (3A .tan a1 (iii) Then the value of resistor 103, defining a slope equal to a quarter of the initial slope, must be made equal to one-sixth of the value of resistor R17, according to Relation ii. This relation gives:

The resistance value which determines a `slope of half the value of the initial slope is the sum of resistances 103 and 102. From Relation ii, the following value of -resistor 102 is obtained:

(V) :Bruits The resistance value which determines a slope which is three-quarters of the value of the initial slope, is the sum of resistances 101, 102 Iand 103. From Relation the following value of the resistor 101 is obtained:

which is comparatively high 'with respect -to any internal resistance of a vacuum tube diode yavailable in present technique.

I claim:

1. ln a transfer arrangement for an electric simulator of an arbitrary function of at least one variable, cornposed of elementary functions each of which represents a portion of -a straight line of predetermined slope, yat least one transfer network including a series attenuator comprising two series connected resistances, Aat least another transfer netWork including unidirectionally conducting means, vari-able direct current vol-tage supply means ,and reference direct current Voltage supply means coupled, respectively, 4to said transfer net-works, at least one voltage limiting branch extending from the junction point of said Iresistances through said unidirectionally conducting means to said reference voltage supply means, a further resistance connecting said unidirectional means to lsaid junction point, further vol-tage limiting branches derived from said junction point and including further unidirectional means connected respectively `at one side to dilerent points along said further resistance, a further voltage supply means connected respectively to Ithe other side of said unidirectionally conducting means and means including a summing amplifier for linearly adding the voltage outputs derived from said series attenuator yand said voltage limiting branch, respectively.

2. Arrangement according to claim 1 wherein said further unidirectionally conducting means are connected substantially with the same direction of conductibility, and wherein said further 'voltage supply means include voltage adjusting means so adjusted that the voltage values thus applied are stepped up `according to values increasing towards said junction point.

References Cited in the file of this patent UNITED STATES PATENTS 2,144,995 Pulvan' Jan. 24, 1939 2,372,017 Rogers Mar. 20, 1945 2,434,155 Haynes Jan. 6, 1948 2,554,905 Hawkins et al. May 27, 1951 2,567,691 Bock et al. Sept. 11, 1951 2,581,124 Moe Jan. 1, 1952 2,769,137 Creusere Oct. 30, 1956 2,831,107 Raymond Apr. 15, 1958 OTHER REFERENCES Nature, vol. 617, pp. 29, January 6, 1951. 

